40x^2+4x+8=0

Solution for 40x^2+4x+8=0 equation:

Simplifying
40x2 + 4x + 8 = 0

Reorder the terms:
8 + 4x + 40x2 = 0

Solving
8 + 4x + 40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + x + 10x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + x + 10x2)' equal to zero and attempt to solve:

Simplifying
2 + x + 10x2 = 0

Solving
2 + x + 10x2 = 0

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
0.2 + 0.1x + x2 = 0.0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 0.1x + -0.2 + x2 = 0.0 + -0.2

Reorder the terms:
0.2 + -0.2 + 0.1x + x2 = 0.0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 0.1x + x2 = 0.0 + -0.2
0.1x + x2 = 0.0 + -0.2

Combine like terms: 0.0 + -0.2 = -0.2
0.1x + x2 = -0.2

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1x + 0.25 + x2 = -0.2 + 0.25

Reorder the terms:
0.25 + 0.1x + x2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
0.25 + 0.1x + x2 = 0.05

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.223606798 and -0.223606798.

Subproblem 1
x + 0.5 = 0.223606798

Simplifying
x + 0.5 = 0.223606798

Reorder the terms:
0.5 + x = 0.223606798

Solving
0.5 + x = 0.223606798

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.223606798 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.223606798 + -0.5
x = 0.223606798 + -0.5

Combine like terms: 0.223606798 + -0.5 = -0.276393202
x = -0.276393202

Simplifying
x = -0.276393202

Subproblem 2
x + 0.5 = -0.223606798

Simplifying
x + 0.5 = -0.223606798

Reorder the terms:
0.5 + x = -0.223606798

Solving
0.5 + x = -0.223606798

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.223606798 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.223606798 + -0.5
x = -0.223606798 + -0.5

Combine like terms: -0.223606798 + -0.5 = -0.723606798
x = -0.723606798

Simplifying
x = -0.723606798

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.276393202, -0.723606798}
Solution
x = {-0.276393202, -0.723606798}